Sep 13 - Super Hard
Puzzle Copyright © Kevin Stone
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Reasoning
R5C7 is the only square in row 5 that can be <7>
Squares R8C5 and R8C6 in row 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the row.
R8C1 - removing <58> from <23578> leaving <237>
R8C2 - removing <8> from <3478> leaving <347>
R8C7 - removing <5> from <2456> leaving <246>
R8C8 - removing <5> from <2345> leaving <234>
R8C9 - removing <5> from <24567> leaving <2467>
Squares R1C6 and R8C6 in column 6 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R3C6 - removing <58> from <1258> leaving <12>
R6C6 - removing <58> from <2458> leaving <24>
Squares R8C5 and R8C6 in block 8 form a simple naked pair. These 2 squares both contain the 2 possibilities <58>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R7C4 - removing <58> from <1578> leaving <17>
R9C4 - removing <5> from <157> leaving <17>
Squares R7C4 and R9C4 in column 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <17>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the column.
R2C4 - removing <1> from <1258> leaving <258>
R4C4 - removing <1> from <12> leaving <2>
R6C6 can only be <4>
R4C6 can only be <1>
R3C6 can only be <2>
R4C9 is the only square in row 4 that can be <4>
R5C2 is the only square in row 5 that can be <1>
R3C1 is the only square in row 3 that can be <1>
R2C5 is the only square in row 2 that can be <1>
R3C2 is the only square in row 3 that can be <7>
Squares R4C1 and R4C3 in block 4 form a simple naked pair. These 2 squares both contain the 2 possibilities <39>. Since each of the squares must contain one of the possibilities, they can be eliminated from the other squares in the block.
R6C1 - removing <9> from <289> leaving <28>
Intersection of column 2 with block 7. The value <3> only appears in one or more of squares R7C2, R8C2 and R9C2 of column 2. These squares are the ones that intersect with block 7. Thus, the other (non-intersecting) squares of block 7 cannot contain this value.
R7C1 - removing <3> from <3578> leaving <578>
R7C3 - removing <3> from <3458> leaving <458>
R8C1 - removing <3> from <237> leaving <27>
Squares R4C1, R4C3, R1C1 and R1C3 form a Type-3 Unique Rectangle on <39>. Upon close inspection, it is clear that:
(R1C1 or R1C3)<58> and R1C6<58> form a naked pair on <58> in row 1. No other squares in the row can contain these possibilities
R1C7 - removing <5> from <59> leaving <9>
R6C9 is the only square in row 6 that can be <9>
R7C8 is the only square in row 7 that can be <9>
R7C2 is the only square in row 7 that can be <3>
R8C2 can only be <4>
R2C2 can only be <8>
R2C4 can only be <5>
R2C1 can only be <9>
R6C4 can only be <8>
R1C6 can only be <8>
R6C1 can only be <2>
R5C5 can only be <5>
R8C6 can only be <5>
R4C1 can only be <3>
R4C3 can only be <9>
R1C1 can only be <5>
R5C8 can only be <2>
R8C5 can only be <8>
R5C3 can only be <8>
R2C8 can only be <4>
R8C8 can only be <3>
R6C7 can only be <5>
R8C1 can only be <7>
R1C3 can only be <3>
R7C1 can only be <8>
R2C3 can only be <6>
R3C8 can only be <5>
R3C7 can only be <6>
R3C3 can only be <4>
R8C7 can only be <2>
R2C9 can only be <2>
R3C9 can only be <8>
R7C3 can only be <5>
R7C9 can only be <7>
R9C3 can only be <2>
R7C4 can only be <1>
R8C9 can only be <6>
R9C7 can only be <1>
R9C9 can only be <5>
R9C4 can only be <7>
R7C7 can only be <4>
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